Problem: Rewrite as a simplified fraction. ${0.2\overline{71} = {?}}$
Answer: Let $x$ equal the decimal. Set up two equations such that the digits after the decimal point are identical. ${\begin{align*}1000x &= 271.7171...\\ 10x &= 2.7171...\end{align*}}$ Subtracting the two equations, we have: ${990x = 269}$ ${x = \dfrac{269}{990}} $